ODE No. 1188

2.1188 ODE No. 1188

$(a x + b) y^{'} (x) + c y (x) + x^{2} y^{″} (x) = 0$ ✓ Mathematica : cpu = 0.0841881 (sec), leaf count = 266

${{y (x) \to c_{1} i^{- \sqrt{a^{2} - 2 a - 4 c + 1} + a - 1} b^{\frac{1}{2} (- \sqrt{a^{2} - 2 a - 4 c + 1} + a - 1)} {(\frac{1}{x})}^{\frac{1}{2} (- \sqrt{a^{2} - 2 a - 4 c + 1} + a - 1)}_{1} F_{1} (\frac{a}{2} - \frac{1}{2} \sqrt{a^{2} - 2 a - 4 c + 1} - \frac{1}{2}; 1 - \sqrt{a^{2} - 2 a - 4 c + 1}; \frac{b}{x}) + c_{2} i^{\sqrt{a^{2} - 2 a - 4 c + 1} + a - 1} b^{\frac{1}{2} (\sqrt{a^{2} - 2 a - 4 c + 1} + a - 1)} {(\frac{1}{x})}^{\frac{1}{2} (\sqrt{a^{2} - 2 a - 4 c + 1} + a - 1)}_{1} F_{1} (\frac{a}{2} + \frac{1}{2} \sqrt{a^{2} - 2 a - 4 c + 1} - \frac{1}{2}; \sqrt{a^{2} - 2 a - 4 c + 1} + 1; \frac{b}{x})}}$

✓ Maple : cpu = 0.168 (sec), leaf count = 135

${y (x) =_C 1 x^{- \frac{1}{2} \sqrt{a^{2} - 2 a - 4 c + 1} - \frac{a}{2} + \frac{1}{2}} M (- \frac{1}{2} + \frac{1}{2} \sqrt{a^{2} - 2 a - 4 c + 1} + \frac{a}{2}, 1 + \sqrt{a^{2} - 2 a - 4 c + 1}, \frac{b}{x}) +_C 2 x^{- \frac{1}{2} \sqrt{a^{2} - 2 a - 4 c + 1} - \frac{a}{2} + \frac{1}{2}} U (- \frac{1}{2} + \frac{1}{2} \sqrt{a^{2} - 2 a - 4 c + 1} + \frac{a}{2}, 1 + \sqrt{a^{2} - 2 a - 4 c + 1}, \frac{b}{x})}$

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